# Geometry of Lie integrability by quadratures

@inproceedings{Cariena2015GeometryOL, title={Geometry of Lie integrability by quadratures}, author={J. F. Cari{\~n}ena and Fernando Falceto and Jacek Grabowski and Manuel Fernandez Ra{\~n}ada}, year={2015} }

In this paper, we extend the Lie theory of integration by quadratures of systems of ordinary differential equations in two different ways. First, we consider a finite-dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way. It turns out that the conditions can be expressed in a purely algebraic way. In the second step, we generalize the construction to the case in… CONTINUE READING

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## Solvability of a Lie algebra of vector fields implies their integrability by quadratures

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## Transitive nilpotent Lie algebras of vector fields and their Tanaka prolongations

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## Solvable Lie algebras of vector fields and a Lie's conjecture

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## Non-commutative integrability, exact solvability and the Hamilton-Jacobi theory

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## Applicable Differential Geometry

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HIGHLY INFLUENTIAL

## The Euler-Jacobi-Lie integrability theorem

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## Remarks on nilpotent Lie algebras of vector fields.

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## Nilpotent Lie algebras of vectorfields.

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